A Hybrid Estimation of Distribution Algorithm and Nelder-Mead Simplex Method for Solving a Class of Nonlinear Bilevel Programming Problems

المؤلفون المشاركون

Jia, Fei
Ren, Aihong
Wang, Yuping

المصدر

Journal of Applied Mathematics

العدد

المجلد 2013، العدد 2013 (31 ديسمبر/كانون الأول 2013)، ص ص. 1-10، 10ص.

الناشر

Hindawi Publishing Corporation

تاريخ النشر

2013-08-13

دولة النشر

مصر

عدد الصفحات

10

التخصصات الرئيسية

الرياضيات

الملخص EN

We propose a hybrid algorithm based on estimation of distribution algorithm (EDA) and Nelder-Mead simplex method (NM) to solve a class of nonlinear bilevel programming problems where the follower’s problem is linear with respect to the lower level variable.

The bilevel programming is an NP-hard optimization problem, for which EDA-NM is applied as a new tool aiming at obtaining global optimal solutions of such a problem.

In fact, EDA-NM is very easy to be implementedsince it does not require gradients information.

Moreover, the hybrid algorithm intends to produce faster and more accurate convergence.

In the proposed approach, for fixed upper level variable, we make use of the optimality conditions of linear programming to deal with the follower’s problem and obtain its optimal solution.

Further, the leader’s objective function is taken as the fitness function.

Based on these schemes, the hybrid algorithm is designed by combining EDA with NM.

To verify the performance of EDA-NM, simulations on some test problems are made, and the results demonstrate that the proposed algorithm has a better performance than the compared algorithms.

Finally, the proposed approach is used to solve a practical example about pollution charges problem.

نمط استشهاد جمعية علماء النفس الأمريكية (APA)

Ren, Aihong& Wang, Yuping& Jia, Fei. 2013. A Hybrid Estimation of Distribution Algorithm and Nelder-Mead Simplex Method for Solving a Class of Nonlinear Bilevel Programming Problems. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-467331

نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)

Ren, Aihong…[et al.]. A Hybrid Estimation of Distribution Algorithm and Nelder-Mead Simplex Method for Solving a Class of Nonlinear Bilevel Programming Problems. Journal of Applied Mathematics No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-467331

نمط استشهاد الجمعية الطبية الأمريكية (AMA)

Ren, Aihong& Wang, Yuping& Jia, Fei. A Hybrid Estimation of Distribution Algorithm and Nelder-Mead Simplex Method for Solving a Class of Nonlinear Bilevel Programming Problems. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-467331

نوع البيانات

مقالات

لغة النص

الإنجليزية

الملاحظات

Includes bibliographical references

رقم السجل

BIM-467331